The proof is almost the same as that of Theorem REF , except for two points.
First, to get well-posedness of the FBSDEs (REF ) and (REF ), we rather use the results in [1]} and [2]} respectively.
Secondly, one should apply the second part of Lemma REF  below, (i.e. the case of \(T\)  arbitrary) to get the bound of \(\sum _{i=1}^N\Vert X^{\underline{\alpha },i} - \mathcal {X}^{i}\Vert ^2_\infty \) .
